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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 5 - Systems and MatricesProblem 73
Chapter 6, Problem 73

Perform each operation, if possible.
[325]−[8−46]+[102]\(\left\)[\(\begin{matrix}\)3\\ 2\\ 5\(\end{matrix}\]\right\)]-\(\left\)[\(\begin{matrix}\)8\\ -4\\ 6\(\end{matrix}\[\right\)]+\(\left\)[\(\begin{matrix}\)1\\ 0\\ 2\(\end{matrix}\]\right\)]

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1
Identify the dimensions of each matrix involved in the operation. Here, all matrices are 1x3, meaning they each have 1 row and 3 columns.
Recall that matrix addition and subtraction are only defined for matrices of the same dimensions. Since all matrices are 1x3, these operations are possible.
Perform the subtraction first: subtract corresponding elements of the first and second 1x3 matrices. If the first matrix is \(A = [a_1, a_2, a_3]\) and the second is \(B = [b_1, b_2, b_3]\), then \(A - B = [a_1 - b_1, a_2 - b_2, a_3 - b_3]\).
Next, add the resulting matrix from the subtraction to the third 1x3 matrix. If the third matrix is \(C = [c_1, c_2, c_3]\), then \((A - B) + C = [(a_1 - b_1) + c_1, (a_2 - b_2) + c_2, (a_3 - b_3) + c_3]\).
Write the final matrix as the result of the operation, which will also be a 1x3 matrix with each element calculated as above.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Matrix Dimensions and Compatibility

Matrix operations like addition and subtraction require the matrices to have the same dimensions. Here, all matrices are 1x3, meaning they each have one row and three columns, so they are compatible for addition and subtraction.
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Introduction to Matrices

Matrix Addition and Subtraction

Matrix addition and subtraction are performed element-wise. For two matrices of the same size, you add or subtract corresponding elements to get the resulting matrix.
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Order of Operations in Matrix Arithmetic

When performing multiple operations, follow the order of operations (left to right for addition and subtraction). First subtract the second matrix from the first, then add the third matrix to the result.
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Related Practice
Textbook Question

Given A=[4−231],B=[510−237]A = \(\left\)[ \(\begin{matrix}\) 4 & -2 \\ 3 & 1 \(\end{matrix}\) \(\right\)], \(\quad\) B = \(\left\)[ \(\begin{matrix}\) 5 & 1 \\ 0 & -2 \\ 3 & 7 \(\end{matrix}\) \(\right\)], and C=[−541036]C = \(\left\)[ \(\begin{matrix}\) -5 & 4 & 1 \\ 0 & 3 & 6 \(\end{matrix}\) \(\right\)], find each product, if possible. See Examples 5–7. AB

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Textbook Question

Perform each operation, if possible.

[258192]−[3471]\(\left\)[ \(\begin{matrix}\) 2 & 5 & 8 \\ 1 & 9 & 2 \(\end{matrix}\) \(\right\)] - \(\left\)[ \(\begin{matrix}\) 3 & 4 \\ 7 & 1 \(\end{matrix}\) \(\right\)]

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Textbook Question

Solve each system. (Hint: In Exercises 69–72, let 1/x=t1/x = t and 1/y=u1/y = u.)

2x+3y=18\(\frac{2}{x}\)+\(\frac{3}{y}\)=18

4x−5y=−8\(\frac{4}{x}\)-\(\frac{5}{y}\)=-8

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Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7.

(1/2)x + (1/3)y = 2

(3/2)x - (1/2)y = -12

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Textbook Question

Consider the following nonlinear system. Work Exercises 75 –80 in order.

y = | x - 1 |

y = x2 - 4

How is the graph of y = | x - 1 | obtained by transforming the graph of y = | x |?

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Textbook Question

Solve each problem. The supply and demand equations for a certain commodity are given. supply: p = √(0.1q + 9) - 2 and demand: p = √(25 - 0.1q).

Find the equilibrium price (in dollars).

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